file_path stringlengths 11 79 | full_name stringlengths 2 100 | traced_tactics list | end list | commit stringclasses 4
values | url stringclasses 4
values | start list |
|---|---|---|---|---|---|---|
Mathlib/Analysis/NormedSpace/Exponential.lean | exp_mem_unitary_of_mem_skewAdjoint | [
{
"state_after": "no goals",
"state_before": "π : Type u_2\nπΈ : Type u_1\nπΉ : Type ?u.368109\ninstββ· : IsROrC π\ninstββΆ : NormedRing πΈ\ninstββ΅ : NormedAlgebra π πΈ\ninstββ΄ : NormedRing πΉ\ninstβΒ³ : NormedAlgebra π πΉ\ninstβΒ² : CompleteSpace πΈ\ninstβΒΉ : StarRing πΈ\ninstβ : ContinuousStar πΈ\nx : πΈ\... | [
492,
57
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
488,
1
] |
Mathlib/MeasureTheory/Decomposition/Jordan.lean | MeasureTheory.SignedMeasure.totalVariation_mutuallySingular_iff | [] | [
598,
40
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
595,
1
] |
Mathlib/Analysis/Convex/Cone/Basic.lean | ConvexCone.salient_iff_not_flat | [
{
"state_after": "no goals",
"state_before": "π : Type u_1\nE : Type u_2\nF : Type ?u.66658\nG : Type ?u.66661\ninstβΒ² : OrderedSemiring π\ninstβΒΉ : AddCommGroup E\ninstβ : SMul π E\nSβ S : ConvexCone π E\nβ’ Salient S β Β¬Flat S",
"tactic": "simp [Salient, Flat]"
}
] | [
388,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
387,
1
] |
Mathlib/Data/Set/Pointwise/Basic.lean | Set.div_union | [] | [
714,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
713,
1
] |
Mathlib/Algebra/Star/Pi.lean | Function.update_star | [] | [
73,
62
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
71,
1
] |
Mathlib/Data/Finset/Lattice.lean | Finset.inf_sdiff_right | [
{
"state_after": "case hβ\nF : Type ?u.200836\nΞ± : Type u_2\nΞ² : Type ?u.200842\nΞ³ : Type ?u.200845\nΞΉ : Type u_1\nΞΊ : Type ?u.200851\ninstβ : BooleanAlgebra Ξ±\ns : Finset ΞΉ\nf : ΞΉ β Ξ±\na : Ξ±\nb : ΞΉ\nβ’ (inf {b} fun b => f b \\ a) = inf {b} f \\ a\n\ncase hβ\nF : Type ?u.200836\nΞ± : Type u_2\nΞ² : Type ?u.200842\... | [
635,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
631,
1
] |
Mathlib/Analysis/Convex/Slope.lean | convexOn_of_slope_mono_adjacent | [
{
"state_after": "π : Type u_1\ninstβ : LinearOrderedField π\ns : Set π\nf : π β π\nhs : Convex π s\nhf : β {x y z : π}, x β s β z β s β x < y β y < z β (f y - f x) / (y - x) β€ (f z - f y) / (z - y)\nx : π\nhx : x β s\nz : π\nhz : z β s\nhxz : x < z\na b : π\nha : 0 < a\nhb : 0 < b\nhab : a + b = 1\ny... | [
132,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
106,
1
] |
Mathlib/AlgebraicGeometry/RingedSpace.lean | AlgebraicGeometry.RingedSpace.mem_top_basicOpen | [
{
"state_after": "no goals",
"state_before": "X : RingedSpace\nf : β(X.presheaf.obj β€.op)\nx : ββX.toPresheafedSpace\nβ’ x β β€",
"tactic": "trivial"
}
] | [
178,
27
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Data/Finset/Image.lean | Finset.map_singleton | [
{
"state_after": "no goals",
"state_before": "Ξ± : Type u_1\nΞ² : Type u_2\nΞ³ : Type ?u.39238\nfβ : Ξ± βͺ Ξ²\ns : Finset Ξ±\nf : Ξ± βͺ Ξ²\na : Ξ±\nβ’ β(map f {a}) = β{βf a}",
"tactic": "simp only [coe_map, coe_singleton, Set.image_singleton]"
}
] | [
224,
78
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
223,
1
] |
Mathlib/CategoryTheory/Action.lean | CategoryTheory.ActionCategory.back_coe | [
{
"state_after": "case mk\nM : Type u_1\ninstβΒΉ : Monoid M\nX : Type u\ninstβ : MulAction M X\nfstβ : SingleObj M\nsndβ : (actionAsFunctor M X).obj fstβ\nβ’ { fst := (), snd := ActionCategory.back { fst := fstβ, snd := sndβ } } = { fst := fstβ, snd := sndβ }",
"state_before": "M : Type u_1\ninstβΒΉ : Monoid M... | [
92,
76
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
92,
1
] |
Mathlib/Topology/Bornology/Basic.lean | Bornology.isCobounded_sInter | [] | [
281,
16
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
279,
1
] |
Mathlib/Data/Complex/Basic.lean | Complex.normSq_conj | [
{
"state_after": "no goals",
"state_before": "z : β\nβ’ βnormSq (β(starRingEnd β) z) = βnormSq z",
"tactic": "simp [normSq]"
}
] | [
652,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
652,
1
] |
Mathlib/Order/SuccPred/Limit.lean | Order.not_isPredLimit_pred | [] | [
310,
89
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
310,
1
] |
Mathlib/Topology/UniformSpace/Completion.lean | CauchyFilter.cauchyFilter_eq | [
{
"state_after": "case mp\nΞ± : Type u_1\ninstβΒ³ : Inhabited Ξ±\ninstβΒ² : UniformSpace Ξ±\ninstβΒΉ : CompleteSpace Ξ±\ninstβ : SeparatedSpace Ξ±\nf g : CauchyFilter Ξ±\nβ’ lim βf = lim βg β (f, g) β π’ (CauchyFilter Ξ±)\n\ncase mpr\nΞ± : Type u_1\ninstβΒ³ : Inhabited Ξ±\ninstβΒ² : UniformSpace Ξ±\ninstβΒΉ : CompleteSpace Ξ±\ni... | [
315,
69
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
287,
1
] |
Mathlib/Order/ConditionallyCompleteLattice/Basic.lean | GaloisConnection.l_csSup | [] | [
1280,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1278,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.image_const_add_Iic | [
{
"state_after": "no goals",
"state_before": "Ξ± : Type u_1\ninstβ : OrderedAddCommGroup Ξ±\na b c : Ξ±\nβ’ (fun x => a + x) '' Iic b = Iic (a + b)",
"tactic": "simp [add_comm]"
}
] | [
266,
92
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
266,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.L1.SimpleFunc.negPart_toSimpleFunc | [
{
"state_after": "Ξ± : Type u_1\nE : Type ?u.357414\nF : Type ?u.357417\nπ : Type ?u.357420\ninstβΒΉβ° : NormedAddCommGroup E\ninstββΉ : NormedAddCommGroup F\nm : MeasurableSpace Ξ±\nΞΌ : Measure Ξ±\ninstββΈ : NormedField π\ninstββ· : NormedSpace π E\ninstββΆ : NormedSpace β E\ninstββ΅ : SMulCommClass β π E\nF' : Type... | [
612,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
604,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_eq_mul_left | [] | [
1019,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1018,
1
] |
Mathlib/Data/Real/ENNReal.lean | ENNReal.mul_left_mono | [] | [
975,
74
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
975,
1
] |
Mathlib/Algebra/Polynomial/BigOperators.lean | Polynomial.natDegree_prod | [
{
"state_after": "R : Type u\nΞΉ : Type w\ns : Finset ΞΉ\ninstβΒΉ : CommSemiring R\ninstβ : NoZeroDivisors R\nf : ΞΉ β R[X]\nt : Multiset R[X]\nh : β (i : ΞΉ), i β s β f i β 0\nβ : Nontrivial R\nβ’ natDegree (β i in s, f i) = β i in s, natDegree (f i)",
"state_before": "R : Type u\nΞΉ : Type w\ns : Finset ΞΉ\ninstβ... | [
320,
28
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
315,
1
] |
Mathlib/Data/Semiquot.lean | Semiquot.mem_pure | [] | [
164,
24
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Mathlib/CategoryTheory/Abelian/NonPreadditive.lean | CategoryTheory.NonPreadditiveAbelian.neg_add | [
{
"state_after": "no goals",
"state_before": "C : Type u\ninstβΒΉ : Category C\ninstβ : NonPreadditiveAbelian C\nX Y : C\na b : X βΆ Y\nβ’ -(a + b) = -a - b",
"tactic": "rw [add_def, neg_sub', add_neg]"
}
] | [
415,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
415,
1
] |
Mathlib/CategoryTheory/Quotient.lean | CategoryTheory.Quotient.comp_right | [
{
"state_after": "no goals",
"state_before": "C : Type u_2\ninstβ : Category C\nr : HomRel C\na b c : C\ng : b βΆ c\naβ bβ : C\nx : a βΆ aβ\nmβ mβ : aβ βΆ bβ\ny : bβ βΆ b\nh : r mβ mβ\nβ’ CompClosure r ((x β« mβ β« y) β« g) ((x β« mβ β« y) β« g)",
"tactic": "simpa using CompClosure.intro x mβ mβ (y β« g) h"
}
] | [
81,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
79,
1
] |
Mathlib/Combinatorics/SimpleGraph/Connectivity.lean | SimpleGraph.Walk.mem_support_nil_iff | [
{
"state_after": "no goals",
"state_before": "V : Type u\nV' : Type v\nV'' : Type w\nG : SimpleGraph V\nG' : SimpleGraph V'\nG'' : SimpleGraph V''\nu v : V\nβ’ u β support nil β u = v",
"tactic": "simp"
}
] | [
591,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
591,
1
] |
Mathlib/Logic/Equiv/Basic.lean | Equiv.Perm.subtypeCongr.left_apply | [
{
"state_after": "no goals",
"state_before": "Ξ΅ : Type u_1\np : Ξ΅ β Prop\ninstβ : DecidablePred p\nep ep' : Perm { a // p a }\nen en' : Perm { a // Β¬p a }\na : Ξ΅\nh : p a\nβ’ β(subtypeCongr ep en) a = β(βep { val := a, property := h })",
"tactic": "simp [Perm.subtypeCongr.apply, h]"
}
] | [
566,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
565,
1
] |
Mathlib/LinearAlgebra/Eigenspace/Basic.lean | Module.End.eigenspace_restrict_eq_bot | [
{
"state_after": "K R : Type v\nV M : Type w\ninstββ΅ : CommRing R\ninstββ΄ : AddCommGroup M\ninstβΒ³ : Module R M\ninstβΒ² : Field K\ninstβΒΉ : AddCommGroup V\ninstβ : Module K V\nf : End R M\np : Submodule R M\nhfp : β (x : M), x β p β βf x β p\nΞΌ : R\nhΞΌp : Disjoint (eigenspace f ΞΌ) p\nβ’ eigenspace (LinearMap.res... | [
433,
90
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
429,
1
] |
Mathlib/LinearAlgebra/SesquilinearForm.lean | LinearMap.flip_separatingRight | [] | [
687,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
685,
1
] |
Std/Data/List/Lemmas.lean | List.exists_mem_cons | [
{
"state_after": "no goals",
"state_before": "Ξ± : Type u_1\np : Ξ± β Prop\na : Ξ±\nl : List Ξ±\nβ’ (β x, x β a :: l β§ p x) β p a β¨ β x, x β l β§ p x",
"tactic": "simp"
}
] | [
218,
56
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
217,
1
] |
Mathlib/RingTheory/Int/Basic.lean | Int.coprime_iff_nat_coprime | [
{
"state_after": "no goals",
"state_before": "a b : β€\nβ’ IsCoprime a b β Nat.coprime (natAbs a) (natAbs b)",
"tactic": "rw [β gcd_eq_one_iff_coprime, Nat.coprime_iff_gcd_eq_one, gcd_eq_natAbs]"
}
] | [
206,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
205,
1
] |
Mathlib/Algebra/Lie/Classical.lean | LieAlgebra.SpecialLinear.sl_non_abelian | [
{
"state_after": "case intro.intro\nn : Type u_1\np : Type ?u.17923\nq : Type ?u.17926\nl : Type ?u.17929\nR : Type uβ\ninstββΆ : DecidableEq n\ninstββ΅ : DecidableEq p\ninstββ΄ : DecidableEq q\ninstβΒ³ : DecidableEq l\ninstβΒ² : CommRing R\ninstβΒΉ : Fintype n\ninstβ : Nontrivial R\nh : 1 < Fintype.card n\nj i : n\n... | [
136,
83
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
128,
1
] |
Mathlib/Order/Filter/Prod.lean | Filter.sup_prod | [
{
"state_after": "Ξ± : Type u_1\nΞ² : Type u_2\nΞ³ : Type ?u.5445\nΞ΄ : Type ?u.5448\nΞΉ : Sort ?u.5451\ns : Set Ξ±\nt : Set Ξ²\nf : Filter Ξ±\ngβ : Filter Ξ²\nfβ fβ : Filter Ξ±\ng : Filter Ξ²\nβ’ Filter.prod (fβ β fβ) g = Filter.prod fβ g β Filter.prod fβ g",
"state_before": "Ξ± : Type u_1\nΞ² : Type u_2\nΞ³ : Type ?u.54... | [
124,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
122,
1
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | continuousMultilinearCurryFin0_apply | [] | [
1707,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1705,
1
] |
Std/Data/String/Lemmas.lean | String.data_dropWhile | [
{
"state_after": "no goals",
"state_before": "p : Char β Bool\ns : String\nβ’ (dropWhile s p).data = List.dropWhile p s.data",
"tactic": "rw [dropWhile_eq]"
}
] | [
1111,
64
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1110,
9
] |
Mathlib/Analysis/NormedSpace/Multilinear.lean | ContinuousMultilinearMap.curry_uncurryRight | [
{
"state_after": "case H.h\nπ : Type u\nΞΉ : Type v\nΞΉ' : Type v'\nn : β\nE : ΞΉ β Type wE\nEβ : ΞΉ β Type wEβ\nE' : ΞΉ' β Type wE'\nEi : Fin (Nat.succ n) β Type wEi\nG : Type wG\nG' : Type wG'\ninstβΒΉβ΄ : Fintype ΞΉ\ninstβΒΉΒ³ : Fintype ΞΉ'\ninstβΒΉΒ² : NontriviallyNormedField π\ninstβΒΉΒΉ : (i : ΞΉ) β NormedAddCommGroup ... | [
1504,
17
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1498,
1
] |
Mathlib/GroupTheory/Submonoid/Operations.lean | MulEquiv.coe_submonoidMap_apply | [] | [
1449,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1447,
1
] |
Mathlib/Analysis/Calculus/Deriv/Prod.lean | hasDerivWithinAt_pi | [] | [
106,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
104,
1
] |
Mathlib/MeasureTheory/Integral/IntervalIntegral.lean | intervalIntegral.integral_non_aestronglyMeasurable_of_le | [
{
"state_after": "no goals",
"state_before": "ΞΉ : Type ?u.11347958\nπ : Type ?u.11347961\nE : Type u_1\nF : Type ?u.11347967\nA : Type ?u.11347970\ninstβΒ² : NormedAddCommGroup E\ninstβΒΉ : CompleteSpace E\ninstβ : NormedSpace β E\na b : β\nf g : β β E\nΞΌ : MeasureTheory.Measure β\nh : a β€ b\nhf : Β¬AEStrongl... | [
525,
61
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
523,
1
] |
Mathlib/Order/Atoms.lean | Set.Ici.isAtom_iff | [
{
"state_after": "Ξ± : Type u_1\nΞ² : Type ?u.6700\ninstβ : PartialOrder Ξ±\na bβ : Ξ±\nb : β(Ici a)\nβ’ β₯ β b β a β βb",
"state_before": "Ξ± : Type u_1\nΞ² : Type ?u.6700\ninstβ : PartialOrder Ξ±\na bβ : Ξ±\nb : β(Ici a)\nβ’ IsAtom b β a β βb",
"tactic": "rw [β bot_covby_iff]"
},
{
"state_after": "Ξ± : Ty... | [
189,
98
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
186,
1
] |
Mathlib/RingTheory/Ideal/QuotientOperations.lean | DoubleQuot.coe_quotQuotMkβ | [] | [
725,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
724,
1
] |
Mathlib/Data/Seq/Parallel.lean | Computation.parallel_congr_right | [] | [
410,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
408,
1
] |
Mathlib/Algebra/Quaternion.lean | Quaternion.normSq_zpow | [] | [
1402,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1401,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean | CategoryTheory.Limits.biproduct.ΞΉ_Ο_self | [
{
"state_after": "no goals",
"state_before": "J : Type w\nC : Type u\ninstβΒ² : Category C\ninstβΒΉ : HasZeroMorphisms C\nf : J β C\ninstβ : HasBiproduct f\nj : J\nβ’ ΞΉ f j β« Ο f j = π (f j)",
"tactic": "simp [biproduct.ΞΉ_Ο]"
}
] | [
419,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
418,
1
] |
Mathlib/SetTheory/Ordinal/Principal.lean | Ordinal.principal_add_of_principal_mul | [
{
"state_after": "case inl\no : Ordinal\nho : Principal (fun x x_1 => x * x_1) o\nhoβ : o β 2\nhoβ : o < 2\nβ’ Principal (fun x x_1 => x + x_1) o\n\ncase inr\no : Ordinal\nho : Principal (fun x x_1 => x * x_1) o\nhoββ : o β 2\nhoβ : o > 2\nβ’ Principal (fun x x_1 => x + x_1) o",
"state_before": "o : Ordinal\n... | [
314,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
305,
1
] |
Mathlib/Algebra/Order/Floor.lean | Int.ceil_eq_on_Ioc' | [
{
"state_after": "no goals",
"state_before": "F : Type ?u.227030\nΞ± : Type u_1\nΞ² : Type ?u.227036\ninstβΒΉ : LinearOrderedRing Ξ±\ninstβ : FloorRing Ξ±\nzβ : β€\naβ : Ξ±\nz : β€\na : Ξ±\nha : a β Ioc (βz - 1) βz\nβ’ ββaβ = βz",
"tactic": "exact_mod_cast ceil_eq_on_Ioc z a ha"
}
] | [
1220,
39
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1219,
1
] |
Mathlib/AlgebraicGeometry/ProjectiveSpectrum/Topology.lean | ProjectiveSpectrum.zeroLocus_univ | [] | [
231,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean | smul_vsub_rev_mem_vectorSpan_pair | [] | [
1275,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1273,
1
] |
Mathlib/Analysis/NormedSpace/PiLp.lean | PiLp.nnnorm_equiv_symm_single | [
{
"state_after": "p : ββ₯0β\nπ : Type ?u.441057\nπ' : Type ?u.441060\nΞΉ : Type u_1\nΞ± : ΞΉ β Type ?u.441068\nΞ² : ΞΉ β Type u_2\ninstββΉ : Fintype ΞΉ\ninstββΈ : Fact (1 β€ p)\ninstββ· : NormedField π\ninstββΆ : NormedField π'\ninstββ΅ : (i : ΞΉ) β SeminormedAddCommGroup (Ξ² i)\ninstββ΄ : (i : ΞΉ) β NormedSpace π (Ξ² i)\nc... | [
848,
85
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
828,
1
] |
Mathlib/LinearAlgebra/Matrix/Adjugate.lean | Matrix.cramer_one | [
{
"state_after": "m : Type u\nn : Type v\nΞ± : Type w\ninstββ΄ : DecidableEq n\ninstβΒ³ : Fintype n\ninstβΒ² : DecidableEq m\ninstβΒΉ : Fintype m\ninstβ : CommRing Ξ±\nA : Matrix n n Ξ±\nb : n β Ξ±\ni j : n\nβ’ β(LinearMap.comp (cramer 1) (LinearMap.single i)) 1 j = β(LinearMap.comp 1 (LinearMap.single i)) 1 j",
"st... | [
136,
49
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
130,
1
] |
Mathlib/Analysis/Convex/Gauge.lean | Balanced.starConvex | [
{
"state_after": "no goals",
"state_before": "π : Type ?u.84393\nE : Type u_1\nF : Type ?u.84399\ninstβΒΉ : AddCommGroup E\ninstβ : Module β E\ns t : Set E\naβ : β\nhs : Balanced β s\nx : E\nhx : x β s\na : β\nhaβ : 0 β€ a\nhaβ : a β€ 1\nβ’ βaβ β€ 1",
"tactic": "rwa [Real.norm_of_nonneg haβ]"
}
] | [
218,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
216,
1
] |
Mathlib/GroupTheory/Subsemigroup/Center.lean | Set.neg_mem_center | [
{
"state_after": "no goals",
"state_before": "M : Type u_1\ninstβ : Ring M\na : M\nha : a β center M\nc : M\nβ’ c * -a = -a * c",
"tactic": "rw [β neg_mul_comm, ha (-c), neg_mul_comm]"
}
] | [
84,
45
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
83,
1
] |
Mathlib/Algebra/QuaternionBasis.lean | QuaternionAlgebra.Basis.j_mul_k | [
{
"state_after": "no goals",
"state_before": "R : Type u_2\nA : Type u_1\nB : Type ?u.31470\ninstββ΄ : CommRing R\ninstβΒ³ : Ring A\ninstβΒ² : Ring B\ninstβΒΉ : Algebra R A\ninstβ : Algebra R B\ncβ cβ : R\nq : Basis A cβ cβ\nβ’ q.j * q.k = -cβ β’ q.i",
"tactic": "rw [β i_mul_j, β mul_assoc, j_mul_i, neg_mul, ... | [
104,
67
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/Data/Multiset/FinsetOps.lean | Multiset.le_ndinsert_self | [] | [
64,
59
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Order/Monotone/Monovary.lean | Monovary.comp_monotone_left | [] | [
164,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
163,
1
] |
Std/Data/Int/Lemmas.lean | Int.sign_eq_one_of_pos | [] | [
1270,
23
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
1268,
1
] |
Mathlib/Data/Polynomial/Derivative.lean | Polynomial.derivative_comp | [
{
"state_after": "case h_add\nR : Type u\nS : Type v\nT : Type w\nΞΉ : Type y\nA : Type z\na b : R\nn : β\ninstβ : CommSemiring R\nq pβ qβ : R[X]\naβΒΉ : βderivative (comp pβ q) = βderivative q * comp (βderivative pβ) q\naβ : βderivative (comp qβ q) = βderivative q * comp (βderivative qβ) q\nβ’ βderivative (comp (... | [
552,
9
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
546,
1
] |
Mathlib/LinearAlgebra/AnnihilatingPolynomial.lean | Polynomial.annIdealGenerator_eq_minpoly | [
{
"state_after": "case pos\nπ : Type u_1\nA : Type u_2\ninstβΒ² : Field π\ninstβΒΉ : Ring A\ninstβ : Algebra π A\na : A\nh : annIdealGenerator π a = 0\nβ’ annIdealGenerator π a = minpoly π a\n\ncase neg\nπ : Type u_1\nA : Type u_2\ninstβΒ² : Field π\ninstβΒΉ : Ring A\ninstβ : Algebra π A\na : A\nh : Β¬annIde... | [
169,
26
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
160,
1
] |
Mathlib/Order/Filter/AtTopBot.lean | Filter.tendsto_atTop_add_left_of_le | [] | [
780,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
778,
1
] |
Mathlib/Analysis/Normed/Ring/Seminorm.lean | RingSeminorm.toFun_eq_coe | [] | [
104,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
103,
1
] |
Mathlib/MeasureTheory/Integral/DivergenceTheorem.lean | MeasureTheory.integral_divergence_of_hasFDerivWithinAt_off_countable_auxβ | [
{
"state_after": "case intro.intro.intro\nE : Type u\ninstβΒ² : NormedAddCommGroup E\ninstβΒΉ : NormedSpace β E\ninstβ : CompleteSpace E\nn : β\nI : Box (Fin (n + 1))\nf : (Fin (n + 1) β β) β Fin (n + 1) β E\nf' : (Fin (n + 1) β β) β (Fin (n + 1) β β) βL[β] Fin (n + 1) β E\ns : Set (Fin (n + 1) β β)\nhs : Set.Cou... | [
247,
96
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
144,
1
] |
Std/Control/ForInStep/Lemmas.lean | ForInStep.bindList_cons' | [
{
"state_after": "no goals",
"state_before": "m : Type u_1 β Type u_2\nΞ± : Type u_3\nΞ² : Type u_1\ninstβΒΉ : Monad m\ninstβ : LawfulMonad m\nf : Ξ± β Ξ² β m (ForInStep Ξ²)\ns : ForInStep Ξ²\na : Ξ±\nl : List Ξ±\nβ’ bindList f (a :: l) s = do\n let x β ForInStep.bind s (f a)\n bindList f l x",
"tactic": "s... | [
42,
71
] | e68aa8f5fe47aad78987df45f99094afbcb5e936 | https://github.com/leanprover/std4 | [
40,
1
] |
Mathlib/MeasureTheory/Integral/Bochner.lean | MeasureTheory.continuousWithinAt_of_dominated | [
{
"state_after": "Ξ± : Type u_2\nE : Type u_3\nFβ : Type ?u.1013642\nπ : Type ?u.1013645\ninstβΒΉβ° : NormedAddCommGroup E\ninstββΉ : NormedSpace β E\ninstββΈ : CompleteSpace E\ninstββ· : NontriviallyNormedField π\ninstββΆ : NormedSpace π E\ninstββ΅ : SMulCommClass β π E\ninstββ΄ : NormedAddCommGroup Fβ\ninstβΒ³ : No... | [
1051,
44
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1044,
1
] |
Mathlib/AlgebraicGeometry/PresheafedSpace/HasColimits.lean | AlgebraicGeometry.PresheafedSpace.map_id_c_app | [
{
"state_after": "no goals",
"state_before": "J : Type u'\ninstβΒΉ : Category J\nC : Type u\ninstβ : Category C\nF : J β₯€ PresheafedSpace C\nj : J\nU : Opens ββ(F.obj j)\nβ’ π β(F.obj j) = (F.map (π j)).base",
"tactic": "simp"
},
{
"state_after": "case mk\nJ : Type u'\ninstβΒΉ : Category J\nC : Ty... | [
67,
48
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
61,
1
] |
src/lean/Init/Data/Nat/Basic.lean | Nat.zero_ne_one | [] | [
430,
29
] | d5348dfac847a56a4595fb6230fd0708dcb4e7e9 | https://github.com/leanprover/lean4 | [
429,
11
] |
Mathlib/Topology/Instances/ENNReal.lean | tsum_lt_tsum_of_nonneg | [] | [
1366,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1364,
1
] |
Mathlib/RingTheory/RootsOfUnity/Complex.lean | Complex.mem_rootsOfUnity | [
{
"state_after": "n : β+\nx : βΛ£\nβ’ βx ^ βn = 1 β β i, i < βn β§ exp (2 * βΟ * I * (βi / ββn)) = βx",
"state_before": "n : β+\nx : βΛ£\nβ’ x β rootsOfUnity n β β β i, i < βn β§ exp (2 * βΟ * I * (βi / ββn)) = βx",
"tactic": "rw [mem_rootsOfUnity, Units.ext_iff, Units.val_pow_eq_pow_val, Units.val_one]"
},... | [
91,
63
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
76,
8
] |
Mathlib/Topology/Support.lean | HasCompactMulSupport.comp_closedEmbedding | [
{
"state_after": "X : Type ?u.15456\nΞ± : Type u_1\nΞ±' : Type u_3\nΞ² : Type u_2\nΞ³ : Type ?u.15468\nΞ΄ : Type ?u.15471\nM : Type ?u.15474\nE : Type ?u.15477\nR : Type ?u.15480\ninstββ΄ : TopologicalSpace Ξ±\ninstβΒ³ : TopologicalSpace Ξ±'\ninstβΒ² : One Ξ²\ninstβΒΉ : One Ξ³\ninstβ : One Ξ΄\ngβ : Ξ² β Ξ³\nf : Ξ± β Ξ²\nfβ : Ξ± β... | [
222,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
217,
1
] |
Mathlib/NumberTheory/Divisors.lean | Nat.eq_properDivisors_of_subset_of_sum_eq_sum | [
{
"state_after": "case zero\ns : Finset β\nhsub : s β properDivisors zero\nβ’ β x in s, x = β x in properDivisors zero, x β s = properDivisors zero\n\ncase succ\ns : Finset β\nnβ : β\nhsub : s β properDivisors (succ nβ)\nβ’ β x in s, x = β x in properDivisors (succ nβ), x β s = properDivisors (succ nβ)",
"sta... | [
358,
14
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
340,
1
] |
Mathlib/Topology/SubsetProperties.lean | QuotientMap.isClopen_preimage | [] | [
1657,
52
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1655,
11
] |
Mathlib/MeasureTheory/Measure/GiryMonad.lean | MeasureTheory.Measure.bind_bind | [
{
"state_after": "case h\nΞ± : Type u_2\nΞ² : Type u_3\ninstβΒ² : MeasurableSpace Ξ±\ninstβΒΉ : MeasurableSpace Ξ²\nΞ³ : Type u_1\ninstβ : MeasurableSpace Ξ³\nm : Measure Ξ±\nf : Ξ± β Measure Ξ²\ng : Ξ² β Measure Ξ³\nhf : Measurable f\nhg : Measurable g\ns : Set Ξ³\nhs : MeasurableSet s\nβ’ ββ(bind (bind m f) g) s = ββ(bind m... | [
196,
51
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
191,
1
] |
Mathlib/LinearAlgebra/Matrix/Block.lean | Matrix.blockTriangular_reindex_iff | [
{
"state_after": "case refine'_1\nΞ± : Type u_3\nΞ² : Type ?u.756\nm : Type u_1\nn : Type u_2\no : Type ?u.765\nm' : Ξ± β Type ?u.770\nn' : Ξ± β Type ?u.775\nR : Type v\ninstβΒΉ : CommRing R\nM N : Matrix m m R\nbβ : m β Ξ±\ninstβ : LT Ξ±\nb : n β Ξ±\ne : m β n\nh : BlockTriangular (β(reindex e e) M) b\nβ’ BlockTriangul... | [
73,
75
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
67,
1
] |
Mathlib/Analysis/Convex/Topology.lean | Convex.openSegment_self_interior_subset_interior | [] | [
201,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
199,
1
] |
Mathlib/Order/Monotone/Monovary.lean | AntivaryOn.comp_antitoneOn_right | [] | [
379,
79
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
377,
1
] |
Mathlib/MeasureTheory/Integral/FundThmCalculus.lean | intervalIntegral.integral_deriv_mul_eq_sub | [] | [
1325,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1319,
1
] |
Mathlib/Data/List/Basic.lean | List.lookmap_none | [] | [
3313,
86
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
3311,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.dual_Ici | [] | [
231,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
230,
1
] |
Mathlib/Data/Set/Intervals/Basic.lean | Set.Ici_injective | [] | [
961,
38
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
960,
1
] |
Mathlib/RingTheory/Polynomial/Chebyshev.lean | Polynomial.Chebyshev.T_mul | [
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.113283\ninstβΒΉ : CommRing R\ninstβ : CommRing S\nβ’ β (n : β), T R (0 * n) = comp (T R 0) (T R n)",
"tactic": "simp"
},
{
"state_after": "no goals",
"state_before": "R : Type u_1\nS : Type ?u.113283\ninstβΒΉ : CommRing R\n... | [
279,
42
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
272,
1
] |
Mathlib/Algebra/BigOperators/Basic.lean | Finset.prod_pi_mulSingle | [] | [
1136,
21
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1133,
1
] |
Mathlib/Data/Set/Intervals/Group.lean | Set.pairwise_disjoint_Ioc_zpow | [
{
"state_after": "no goals",
"state_before": "Ξ± : Type u_1\ninstβ : OrderedCommGroup Ξ±\na b : Ξ±\nβ’ Pairwise (Disjoint on fun n => Ioc (b ^ n) (b ^ (n + 1)))",
"tactic": "simpa only [one_mul] using pairwise_disjoint_Ioc_mul_zpow 1 b"
}
] | [
213,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
211,
1
] |
Mathlib/Topology/Connected.lean | mem_connectedComponent | [] | [
597,
82
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
596,
1
] |
Mathlib/Data/Pi/Algebra.lean | Function.extend_inv | [
{
"state_after": "no goals",
"state_before": "I : Type u\nΞ± : Type u_3\nΞ² : Type u_2\nΞ³ : Type u_1\nfβ : I β Type vβ\ngβ : I β Type vβ\nh : I β Type vβ\nx y : (i : I) β fβ i\ni : I\ninstβ : Inv Ξ³\nf : Ξ± β Ξ²\ng : Ξ± β Ξ³\ne : Ξ² β Ξ³\nβ’ extend f gβ»ΒΉ eβ»ΒΉ = (extend f g e)β»ΒΉ",
"tactic": "classical\nfunext x\nsi... | [
386,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
382,
1
] |
Mathlib/Data/List/Chain.lean | List.Chain'.imp | [
{
"state_after": "no goals",
"state_before": "Ξ± : Type u\nΞ² : Type v\nR r : Ξ± β Ξ± β Prop\nlβ lβ lβ : List Ξ±\na b : Ξ±\nS : Ξ± β Ξ± β Prop\nH : β (a b : Ξ±), R a b β S a b\nl : List Ξ±\np : Chain' R l\nβ’ Chain' S l",
"tactic": "cases l <;> [trivial; exact Chain.imp H p]"
}
] | [
177,
64
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
176,
1
] |
Mathlib/Analysis/Calculus/FormalMultilinearSeries.lean | FormalMultilinearSeries.removeZero_coeff_succ | [] | [
107,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
105,
1
] |
Mathlib/RingTheory/Bezout.lean | IsBezout.gcd_eq_sum | [
{
"state_after": "R : Type u\ninstβΒΉ : CommRing R\ninstβ : IsBezout R\nx y : R\nβ’ gcd x y β Ideal.span {gcd x y}",
"state_before": "R : Type u\ninstβΒΉ : CommRing R\ninstβ : IsBezout R\nx y : R\nβ’ gcd x y β Ideal.span {x, y}",
"tactic": "rw [β span_gcd]"
},
{
"state_after": "case a\nR : Type u\ni... | [
86,
77
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
85,
1
] |
Mathlib/Data/Set/Pointwise/Interval.lean | Set.preimage_const_sub_Ioc | [
{
"state_after": "no goals",
"state_before": "Ξ± : Type u_1\ninstβ : OrderedAddCommGroup Ξ±\na b c : Ξ±\nβ’ (fun x => a - x) β»ΒΉ' Ioc b c = Ico (a - c) (a - b)",
"tactic": "simp [β Ioi_inter_Iic, β Ici_inter_Iio, inter_comm]"
}
] | [
252,
54
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
251,
1
] |
Mathlib/MeasureTheory/Function/LpSpace.lean | MeasureTheory.Lp.nnnorm_neg | [
{
"state_after": "no goals",
"state_before": "Ξ± : Type u_1\nE : Type u_2\nF : Type ?u.416520\nG : Type ?u.416523\nm m0 : MeasurableSpace Ξ±\np : ββ₯0β\nq : β\nΞΌ Ξ½ : Measure Ξ±\ninstβΒ² : NormedAddCommGroup E\ninstβΒΉ : NormedAddCommGroup F\ninstβ : NormedAddCommGroup G\nf : { x // x β Lp E p }\nβ’ β-fββ = βfββ",
... | [
350,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
349,
1
] |
Mathlib/Topology/Algebra/Order/LeftRightLim.lean | Monotone.le_rightLim | [] | [
136,
23
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
135,
1
] |
Mathlib/GroupTheory/Subgroup/Basic.lean | Subgroup.NormalizerCondition.normal_of_coatom | [] | [
2259,
73
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2257,
1
] |
Mathlib/Topology/Algebra/Nonarchimedean/Bases.lean | RingSubgroupsBasis.mem_addGroupFilterBasis_iff | [] | [
136,
10
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
134,
1
] |
Mathlib/Order/Lattice.lean | AntitoneOn.sup | [] | [
1217,
58
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
1215,
11
] |
Mathlib/Data/Finset/Prod.lean | Finset.product_union | [
{
"state_after": "case a.mk\nΞ± : Type u_1\nΞ² : Type u_2\nΞ³ : Type ?u.73473\ns s' : Finset Ξ±\nt t' : Finset Ξ²\na : Ξ±\nb : Ξ²\ninstβΒΉ : DecidableEq Ξ±\ninstβ : DecidableEq Ξ²\nx : Ξ±\ny : Ξ²\nβ’ (x, y) β s ΓΛ’ (t βͺ t') β (x, y) β s ΓΛ’ t βͺ s ΓΛ’ t'",
"state_before": "Ξ± : Type u_1\nΞ² : Type u_2\nΞ³ : Type ?u.73473\ns s'... | [
243,
50
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
241,
1
] |
Mathlib/Analysis/Analytic/Linear.lean | ContinuousLinearMap.fpowerSeries_apply_add_two | [] | [
44,
6
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
43,
1
] |
Mathlib/Algebra/CubicDiscriminant.lean | Cubic.card_roots_le | [
{
"state_after": "R : Type u_1\nS : Type ?u.686853\nF : Type ?u.686856\nK : Type ?u.686859\nP : Cubic R\ninstβΒ³ : CommRing R\ninstβΒ² : CommRing S\nΟ : R β+* S\ninstβΒΉ : IsDomain R\ninstβ : DecidableEq R\nβ’ βcard (Polynomial.roots (toPoly P)) β€ 3",
"state_before": "R : Type u_1\nS : Type ?u.686853\nF : Type ... | [
499,
71
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
495,
1
] |
Mathlib/Data/Nat/Cast/Field.lean | Nat.inv_pos_of_nat | [] | [
64,
66
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
63,
1
] |
Mathlib/Analysis/NormedSpace/AffineIsometry.lean | AffineIsometryEquiv.map_ne | [] | [
656,
19
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
655,
1
] |
Mathlib/CategoryTheory/Limits/Shapes/Pullbacks.lean | CategoryTheory.Limits.inl_inl_pushoutAssoc_hom | [
{
"state_after": "C : Type u\ninstββ΅ : Category C\nD : Type uβ\ninstββ΄ : Category D\nW X Y Z Xβ Xβ Xβ Zβ Zβ : C\ngβ : Zβ βΆ Xβ\ngβ : Zβ βΆ Xβ\ngβ : Zβ βΆ Xβ\ngβ : Zβ βΆ Xβ\ninstβΒ³ : HasPushout gβ gβ\ninstβΒ² : HasPushout gβ gβ\ninstβΒΉ : HasPushout (gβ β« pushout.inr) gβ\ninstβ : HasPushout gβ (gβ β« pushout.inl)\nβ’ pu... | [
2606,
33
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
2598,
1
] |
Mathlib/Data/Finset/Fold.lean | Finset.fold_image_idem | [
{
"state_after": "case empty\nΞ± : Type u_1\nΞ² : Type u_3\nΞ³ : Type u_2\nop : Ξ² β Ξ² β Ξ²\nhc : IsCommutative Ξ² op\nha : IsAssociative Ξ² op\nf : Ξ± β Ξ²\nb : Ξ²\ns : Finset Ξ±\na : Ξ±\ninstβ : DecidableEq Ξ±\ng : Ξ³ β Ξ±\nhi : IsIdempotent Ξ² op\nβ’ fold op b f (image g β
) = fold op b (f β g) β
\n\ncase cons\nΞ± : Type u_1\nΞ²... | [
137,
36
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
131,
1
] |
Mathlib/MeasureTheory/Function/LpSeminorm.lean | MeasureTheory.snormEssSup_le_of_ae_bound | [] | [
428,
88
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
426,
1
] |
Mathlib/Topology/Maps.lean | IsClosedMap.of_inverse | [
{
"state_after": "Ξ± : Type u_2\nΞ² : Type u_1\nΞ³ : Type ?u.198659\nΞ΄ : Type ?u.198662\ninstβΒ² : TopologicalSpace Ξ±\ninstβΒΉ : TopologicalSpace Ξ²\ninstβ : TopologicalSpace Ξ³\nf : Ξ± β Ξ²\nf' : Ξ² β Ξ±\nh : Continuous f'\nl_inv : LeftInverse f f'\nr_inv : Function.RightInverse f f'\ns : Set Ξ±\nhs : IsClosed s\nβ’ IsClos... | [
501,
22
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
498,
1
] |
Mathlib/LinearAlgebra/AffineSpace/FiniteDimensional.lean | collinear_insert_of_mem_affineSpan_pair | [
{
"state_after": "k : Type u_2\nV : Type u_3\nP : Type u_1\nΞΉ : Type ?u.322022\ninstβΒ³ : DivisionRing k\ninstβΒ² : AddCommGroup V\ninstβΒΉ : Module k V\ninstβ : AffineSpace V P\npβ pβ pβ : P\nh : pβ β affineSpan k {pβ, pβ}\nβ’ Collinear k {pβ, pβ}",
"state_before": "k : Type u_2\nV : Type u_3\nP : Type u_1\nΞΉ ... | [
559,
29
] | 5a919533f110b7d76410134a237ee374f24eaaad | https://github.com/leanprover-community/mathlib4 | [
556,
1
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.